We study the problem of online learning in competitive settings in the context of two-sided matching markets.

To solve this problem, convergent algorithms are developed with both single-loop and stochastic variants. Notably, this is the firstsingle-loop primalalgorithmforconstrained optimization toourknowledge.

Inthisconte the (asymptotic) derived [68].

Active inference is a unifying theory for perception and action resting upon the idea that the brain maintains an internal model of the world by minimizing free energy.